what type of rendering engine is cycles
Cycles is a ray tracing renderer.
Can use different tracing strategies (under integrator option):


Path tracing: pure path tracer.
Branched path tracing: path tracer with branching on the first bounce.


It uses Monte-Carlo for sampling, that means repeated random sampling.

Soon Metropolis Light Transport should be also available which is a variant to Monte-Carlo, it uses Bidirectional path tracing and Metropolis sampling.